When Does an Observer Become an Inertial Observer?

Dec 2012
76
4
Boulder, Colorado
Inertial observers can legitimately use the famous time-dilation result of special relativity to determine simultaneity at a distance. Observers who are currently accelerating can't.

To be an inertial observer during some period of your life, do you have to be a PERPETUALLY inertial observer? I.e., is it required that you must NEVER have accelerated in the past, and that you can guarantee that you will NEVER accelerate in the future?

Or, can you be an inertial observer if it has been long enough since you stopped accelerating, and if you can guarantee that you will not accelerate for some period of time into the future?

Or, can you be an inertial observer for some period of time, provided that you don't accelerate during that period?

The question matters, because the answer specifies WHO is entitled to use the famous time-dilation result, and WHEN can they use it, in order to determine simultaneity at a distance.

Different answers to that question have produced several different published procedures for answering the question, "How old is that particular distant person, who is moving with respect to me, RIGHT NOW?".

Dolby and Gull, in their "Radar Simultaneity", say that an observer is an inertial observer if he has not accelerated too recently, and will not accelerate too far into the future (and they exactly specify how much is too much). Dolby and Gull's method is clearly non-causal.

Minguzzi says that an observer is an inertial observer if he hasn't accelerated too recently, but there is no requirement that he can't accelerate at any time in the future.

The "Momentarily Co-Moving Inertial Frames Montage" (MCMIFM) says that an observer is an inertial observer if he isn't CURRENTLY accelerating, even if he has accelerated infinitesimally-recently in the past, or will accelerate infinitesimally-soon in the future ... i.e., he can use the time dilatation result throughout any period of time in which he is not accelerating.

What say you?
 

topsquark

Forum Staff
Apr 2008
2,978
631
On the dance floor, baby!
Inertial observers can legitimately use the famous time-dilation result of special relativity to determine simultaneity at a distance. Observers who are currently accelerating can't.

To be an inertial observer during some period of your life, do you have to be a PERPETUALLY inertial observer? I.e., is it required that you must NEVER have accelerated in the past, and that you can guarantee that you will NEVER accelerate in the future?

Or, can you be an inertial observer if it has been long enough since you stopped accelerating, and if you can guarantee that you will not accelerate for some period of time into the future?

Or, can you be an inertial observer for some period of time, provided that you don't accelerate during that period?

The question matters, because the answer specifies WHO is entitled to use the famous time-dilation result, and WHEN can they use it, in order to determine simultaneity at a distance.

Different answers to that question have produced several different published procedures for answering the question, "How old is that particular distant person, who is moving with respect to me, RIGHT NOW?".

Dolby and Gull, in their "Radar Simultaneity", say that an observer is an inertial observer if he has not accelerated too recently, and will not accelerate too far into the future (and they exactly specify how much is too much). Dolby and Gull's method is clearly non-causal.

Minguzzi says that an observer is an inertial observer if he hasn't accelerated too recently, but there is no requirement that he can't accelerate at any time in the future.

The "Momentarily Co-Moving Inertial Frames Montage" (MCMIFM) says that an observer is an inertial observer if he isn't CURRENTLY accelerating, even if he has accelerated infinitesimally-recently in the past, or will accelerate infinitesimally-soon in the future ... i.e., he can use the time dilatation result throughout any period of time in which he is not accelerating.

What say you?
I mostly agree with the MCMIFM idea. But I have no idea why anyone would care that a frame is going to or has already accelerate at some point in the past or future. As long as it is not accelerating it should be an inertial frame.

I have heard of a case where we can break any motion into differential elements and say that at one instant we have this inertial frame which changes over time. I really don't know anything about that system. I would think that the full GR would be more applicable in that case anyway.

-Dan
 
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Dec 2012
76
4
Boulder, Colorado
I mostly agree with the MCMIFM idea. But I have no idea why anyone would care that a frame is going to or has already accelerated at some point in the past or future. As long as it is not accelerating it should be an inertial frame.
In my opinion, physicists who put other restrictions on what is required for an observer to be an inertial observer, do so because they know that the MCMIFM assumption leads to the conclusion that, if the traveling twin suddenly increases his velocity in the direction AWAY from the home twin, that the home twin will suddenly get YOUNGER (according to the traveler). They find that result so ABHORRENT that they impose other restrictions on the definition of an inertial observer, in order to eliminate the possibility of negative ageing.
 
Jun 2016
1,198
566
England
By their actions shall ye know them.

An inertial observer is one for whom the experiments, that require an inertial observation frame, work.
A non-inertial observer is one for whom those same experiments don't work.
 
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